An object moving in a liquid experiences a linear drag force: vector D = (bv, di
ID: 2106236 • Letter: A
Question
An object moving in a liquid experiences a linear drag force: vector D = (bv, direction opposite the motion), where b is a constant called drag coefficient. For a sphere of radius R, the drag constant can be computed as b = (6) pi (eta) R, where eta is the viscosity of the liquid. Water at 20 degrees celsius has eta = 0.001 Newton second/ meter squared. Suppose a 4.6 centimeter diameter, 37 gram ball is shot horizontally into tank of 20 degree water. How long will it take for the horizontal speed todecrease to 50% of its initial value entering the tank? Another helpful equation v(t) = v(0) e ^ ( -6*pi* radius * eta * time/ mass)
bonus 300 points
Explanation / Answer
using the secong equaiton and putting V(t)=.5V(0)
we get .5=e^(-6*pi*radius*eta*time/mass)
taking Ln   Ln(.5)=-6*pi*radius*eta*time/mass
radius= .046/2 , mass= .037 kgs
gives time = 59.156 seconlds